I finally found the Pin and Code Compatibility Chart at the back of the
Microchip line card.

So I see that the 16F76 and the 16F876 are CODE and PIN compatible.

A cursory glance at the two data sheets say they're pretty similar.

I see in the line card that the 16F76 has other feature: Self-read
whereas the 16F876 has Self-programming.

Can anyone tell me why they make the two parts if they're almost
identical?

Failing that can anyone explain the chip numbering system?

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Take a closer look.. aside from what Wouter said (EEPROM and code
memory), the A/D is only 8-bits on the F76 vs. 10 bits on the 876.

>Can anyone tell me why they make the two parts if they're almost
>identical?

I'd guess it's a business reason rather than technical, they can
sell the F76 for cheaper if they want, because it is a stripped
version. They make more money total by offering two versions, even if
the cheaper one costs about the same to make. The book price difference
is very small, about 4.5% in 100's and 1% in 10K. But for negotiated
price you might find a bigger difference.

The best place to start is the line card. If it's a high volume product
then a price list also helps, but if it's a one-off or hobby project then
any PIC is cheap enough.

> So I see that the 16F76 and the 16F876 are CODE and PIN compatible.

Just about all 28 pin parts are pin compatible. Microchip further claims
that everything within a family is "code compatible", but those are
marketing words. Different parts have different amounts of RAM, different
mix of peripherals, special function registers, etc, but are still "code
compatible".

> I see in the line card that the 16F76 has other feature: Self-read
> whereas the 16F876 has Self-programming.
>
> Can anyone tell me why they make the two parts if they're almost
> identical?

I'm guessing the 16F76 is a little cheaper, but I haven't looked it up.

> Failing that can anyone explain the chip numbering system?

It has something to do with a dead fish, the full moon, and a chicken.